The Timberwolves slaughtered Miami 52-24 on the boards, with Kevin Love winning 18 of the rebounds and Montenegrin Nikola Pekovic 12.
But the Heat shrugged off the disadvantage as they dominated the turnover count, and were never threatened after pulling away in the second half.
"I don't know how many times I've seen that, when you get doubled up on the rebounding and you still win," Heat head coach Erik Spoelstra told reporters.
"We'll take it."
LeBron James put up 22 points with 11 assists and seven rebounds in his 42 minutes on court to notch his 27th consecutive regular season game with at least 20 points.
The visitors led 27-21 at the end of the first quarter, having dominated the rebounds 18-3 in the opening 12 minutes.
Miami recovered to lead 52-49 at the half, with Mario Chalmers scoring a three-pointer with the final play.
The Heat took control after the break, with James scoring 14 points, and overhauled the largest rebounding deficit in their history.
"They were absolutely annihilating us on the glass," said Spoelstra.
"In the second half it felt we did a better job but they still had opportunities with second chance points. The only thing we could do at that point was put bodies on them and tip the ball away to somebody else," he said.
The Heat forced 20 turnovers for a second consecutive game, yielding 25 points, and made 14 blocked shots and 12 steals.
"You have to make up for (the rebounding) somewhere else," said Miami forward Shane Battier.
"It's not a way we would want to rest ourselves every night but if you play hard in other areas of the game, force turnovers and are efficient on the offensive end, you can mitigate that a little bit," he said.
Chris Bosh said the Heat had shown their quality in overcoming their rebounding weakness, a problem throughout the season.
"We're a good team. Good teams always find a way to win. We have to find a way to rebound collectively as a unit. Once we start doing that we give ourselves a better chance to win," he said.
"When we get to that point we can really start to squeeze the life out of teams slowly but surely."(Editing by Ian Ransom)